Cryptographic attack is a threat to information systems in the field of public security. SCA can decrypt encrypted information by non-invasively analyzing EM emissions leaked from encryption devices. Compared to other cryptographic attack, it is more covert and broadly applicable. Traditional SCA methods based on signal processing are difficult to conduct in environments that are more complex or have lower SNR. Neural network-based SCA methods have the capability to automatically extract features from data. However, research in this area is still in its infancy, encountering challenges with accuracy and efficiency. The paper proposes an LSTM-MLP neural network approach for the 256-class classification problem of AES-128 EM SCA. The proposed method combines LSTM and MLP to extract both temporal and static features from the signals, facilitating accurate and efficient decryption of encrypted information. Additionally, to address the interpretability challenges of neural networks, this paper analyzes the interpretability of the proposed model based on LIME. This enhances the reliability of feature extraction from the dataset. The experiments in this paper confirm that the proposed method can accurately decrypt encrypted keys under various conditions. Furthermore, the network has fewer parameters, which implies higher efficiency. The interpretability analysis based on LIME also improves the accuracy of the SCA.